Question: Simplify the following expression: $ k = \dfrac{10}{-9y - 6} + \dfrac{-5}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{10}{-9y - 6} \times \dfrac{7}{7} = \dfrac{70}{-63y - 42} $ Multiply the second expression by $\dfrac{-9y - 6}{-9y - 6}$ $ \dfrac{-5}{7} \times \dfrac{-9y - 6}{-9y - 6} = \dfrac{45y + 30}{-63y - 42} $ Therefore $ k = \dfrac{70}{-63y - 42} + \dfrac{45y + 30}{-63y - 42} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{70 + 45y + 30}{-63y - 42} $ $k = \dfrac{45y + 100}{-63y - 42}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{-45y - 100}{63y + 42}$